/*
** License Applicability. Except to the extent portions of this file are
** made subject to an alternative license as permitted in the SGI Free
** Software License B, Version 1.1 (the "License"), the contents of this
** file are subject only to the provisions of the License. You may not use
** this file except in compliance with the License. You may obtain a copy
** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
**
** http://oss.sgi.com/projects/FreeB
**
** Note that, as provided in the License, the Software is distributed on an
** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
**
** Original Code. The Original Code is: OpenGL Sample Implementation,
** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
** Copyright in any portions created by third parties is as indicated
** elsewhere herein. All Rights Reserved.
**
** Additional Notice Provisions: The application programming interfaces
** established by SGI in conjunction with the Original Code are The
** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
** Window System(R) (Version 1.3), released October 19, 1998. This software
** was created using the OpenGL(R) version 1.2.1 Sample Implementation
** published by SGI, but has not been independently verified as being
** compliant with the OpenGL(R) version 1.2.1 Specification.
**
*/
/*
 *
 * OpenGL ES 1.0 CM port of GLU by Mike Gorchak <mike@malva.ua>
*/

#include <stdlib.h>
#include <stdio.h>
#include <assert.h>
#include <math.h>

#include "bezierEval.h"

#ifdef __WATCOMC__
   #pragma warning 14  10
#endif

#define TOLERANCE 0.0001

#ifndef MAX_ORDER
   #define MAX_ORDER 16
#endif

#ifndef MAX_DIMENSION
   #define MAX_DIMENSION 4
#endif

static void normalize(float vec[3]);
static void crossProduct(float x[3], float y[3], float ret[3]);

static float binomialCoefficients[8][8]=
{
   {1, 0, 0,  0,  0,  0,  0, 0},
   {1, 1, 0,  0,  0,  0,  0, 0},
   {1, 2, 1,  0,  0,  0,  0, 0},
   {1, 3, 3,  1,  0,  0,  0, 0},
   {1, 4, 6,  4,  1,  0,  0, 0},
   {1, 5, 10, 10, 5,  1,  0, 0},
   {1, 6, 15, 20, 15, 6,  1, 0},
   {1, 7, 21, 35, 35, 21, 7, 1}
};

void bezierCurveEval(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
{
   float  uprime=(u-u0)/(u1-u0);
   float* ctlptr=ctlpoints;
   float  oneMinusX=1.0f-uprime;
   float  XPower=1.0f;

   int i, k;

   for(k=0; k<dimension; k++)
   {
      retpoint[k]=(*(ctlptr+k));
   }

   for(i=1; i<order; i++)
   {
      ctlptr+=stride;
      XPower*=uprime;
      for(k=0; k<dimension; k++)
      {
         retpoint[k]=retpoint[k]*oneMinusX+ctlptr[k]*binomialCoefficients[order-1][i]*XPower;
      }
   }
}

/* order = degree +1 >=1. */
void bezierCurveEvalDer(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retDer[])
{
   int i, k;
   float  width=u1-u0;
   float* ctlptr=ctlpoints;
   float buf[MAX_ORDER][MAX_DIMENSION];

   if (order==1)
   {
      for(k=0; k<dimension; k++)
      {
         retDer[k]=0;
      }
   }

   for(i=0; i<order-1; i++)
   {
      for(k=0; k<dimension; k++)
      {
         buf[i][k]=(ctlptr[stride+k]-ctlptr[k])*(order-1)/width;
      }
      ctlptr+=stride;
   }

   bezierCurveEval(u0, u1, order-1, (float*)buf, MAX_DIMENSION,  dimension, u, retDer);
}

void bezierCurveEvalDerGen(int der, float u0, float u1, int order, float* ctlpoints, int stride,  int dimension, float u, float retDer[])
{
   int i, k, r;
   float* ctlptr = ctlpoints;
   float  width=u1-u0;
   float  buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];

   if (der<0)
   {
      der=0;
   }

   for(i=0; i<order; i++)
   {
      for(k=0; k<dimension; k++)
      {
         buf[0][i][k]=ctlptr[k];
      }
      ctlptr+=stride;
   }

   for(r=1; r<=der; r++)
   {
      for(i=0; i<order-r; i++)
      {
         for(k=0; k<dimension; k++)
         {
            buf[r][i][k]=(buf[r-1][i+1][k]-buf[r-1][i][k])*(order-r)/width;
         }
      }
   }

   bezierCurveEval(u0, u1, order-der, (float*)(buf[der]), MAX_DIMENSION, dimension, u, retDer);
}

/* the Bezier bivarite polynomial is:
 * sum[i:0,uorder-1][j:0,vorder-1] { ctlpoints[i*ustride+j*vstride] * B(i)*B(j)
 * where B(i) and B(j) are basis functions
 */
void bezierSurfEvalDerGen(int uder, int vder, float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float ret[])
{
   int i;
   float newPoints[MAX_ORDER][MAX_DIMENSION];

   for(i=0; i<uorder; i++)
   {
      bezierCurveEvalDerGen(vder, v0, v1, vorder, ctlpoints+ustride*i, vstride, dimension, v, newPoints[i]);
   }

   bezierCurveEvalDerGen(uder, u0, u1, uorder, (float *) newPoints, MAX_DIMENSION, dimension, u, ret);
}


/* division by w is performed */
void bezierSurfEval(float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float ret[])
{
   bezierSurfEvalDerGen(0, 0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, ret);
   if (dimension==4) /* homogeneous */
   {
      ret[0]/=ret[3];
      ret[1]/=ret[3];
      ret[2]/=ret[3];
   }
}

void bezierSurfEvalNormal(float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float retNormal[])
{
   float partialU[4];
   float partialV[4];
   assert(dimension>=3 && dimension <=4);
   bezierSurfEvalDerGen(1,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialU);
   bezierSurfEvalDerGen(0,1, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialV);

   if (dimension == 3) /* inhomogeneous */
   {
      crossProduct(partialU, partialV, retNormal);
      normalize(retNormal);
      return;
   }
   else /* homogeneous */
   {
      float val[4]; /* the point coordinates (without derivative) */
      float newPartialU[MAX_DIMENSION];
      float newPartialV[MAX_DIMENSION];
      int i;

      bezierSurfEvalDerGen(0,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, val);

      for(i=0; i<=2; i++)
      {
         newPartialU[i]=partialU[i]*val[3]-val[i]*partialU[3];
         newPartialV[i]=partialV[i]*val[3]-val[i]*partialV[3];
      }
      crossProduct(newPartialU, newPartialV, retNormal);
      normalize(retNormal);
   }
}

/* if size is 0, then nothing is done */
static void normalize(float vec[3])
{
   float size=(float)sqrt(vec[0]*vec[0]+vec[1]*vec[1]+vec[2]*vec[2]);

   if (size<TOLERANCE)
   {
      return;
   }
   else
   {
      vec[0]=vec[0]/size;
      vec[1]=vec[1]/size;
      vec[2]=vec[2]/size;
   }
}

static void crossProduct(float x[3], float y[3], float ret[3])
{
   ret[0]=x[1]*y[2]-y[1]*x[2];
   ret[1]=x[2]*y[0]-y[2]*x[0];
   ret[2]=x[0]*y[1]-y[0]*x[1];
}
